Adaptive Spatiotemporal Dimension Reduction in Concurrent Multiscale Damage Analysis

, Computational Mechanics

Recommended citation: Deng, Shiguang, Diran Apelian, Ramin Bostanabad. Computational Mechanics 72 (2023), 3–35.

Abstract: Concurrent multiscale damage models are often used to quantify the impacts of manufacturing-induced micro-porosity on the damage response of macroscopic metallic components. However, these models are challenged by major numerical issues including mesh dependency, convergence difficulty, and low accuracy in concentration regions. In this paper, we make two contributions to address these difficulties. Firstly, we develop a novel adaptive assembly-free implicit-explicit (AAF-IE) temporal integration scheme for nonlinear constitutive models. This scheme prevents the convergence issues that implicit algorithms face amid softening. Our AAF-IE scheme autonomously adjusts step sizes to capture intricate history-dependent deformations. It also dispenses with re-assembling the stiffness matrices in elasto-plasticity and damage models which, in turn, dramatically reduces memory footprints. Secondly, we propose an adaptive clustering-based domain decomposition strategy to dramatically reduce the spatial degrees of freedom by agglomerating close-by finite element nodes into a limited number of clusters. Our adaptive clustering scheme has static and dynamic stages that are carried out during offline and online analyses, respectively. The adaptive strategy updates the cluster density based on the spatial discontinuity of the plastic strain. As demonstrated by numerical experiments, the proposed adaptive method strikes a good balance between efficiency and accuracy for fracture simulations. In particular, we use our efficient concurrent multiscale model to quantify the significance of spatially varying microscopic porosity on a macrostructure’s softening behavior.